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• W2055197892 abstract "Shibakov proved in 1998 that every sequential topological group with a point-countable k -network is metrizable if its sequential order is less than ω 1 . In this paper, we study further topological properties of sequential topological groups with a point-countable k -network. We introduce the notion of a cs -cover, and show that: If G is a sequential topological group with a point-countable cs -cover F such that any product of finitely many elements of F is Lindelöf, then G has an open subgroup which is the union of countably many elements of F . In addition, we show that every topological group with a σ -hereditarily closure-preserving k -network is an ℵ -space." @default.
• W2055197892 created "2016-06-24" @default.
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• W2055197892 date "2002-04-01" @default.
• W2055197892 modified "2023-09-29" @default.
• W2055197892 title "Topological groups with a certain point-countable cover" @default.
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• W2055197892 doi "https://doi.org/10.1016/s0166-8641(01)00066-9" @default.
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